Contents Online
Mathematical Research Letters
Volume 29 (2022)
Number 4
Inverse mean curvature flow over non-star-shaped surfaces
Pages: 1065 – 1086
DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n4.a7
Author
Abstract
We derive an upper bound on the waiting time for a variational weak solution to Inverse Mean Curvature Flow in $\mathbb{R}^{n+1}$ to become star-shaped. As a consequence, we demonstrate that any connected surface moving by the flow which is not initially a topological sphere develops a singularity or self-intersection within a prescribed time interval depending only on initial data. Finally, we establish the existence of either finite-time singularities or intersections for certain topological spheres under IMCF.
Received 6 February 2020
Accepted 18 August 2020
Published 23 February 2023